| 陈焕艮.置换环的Pierce群[J].数学年刊A辑,2009,30(3):391~400 |
| 置换环的Pierce群 |
| Pierce Groups of Exchange Rings |
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| DOI： |
| 中文关键词: Pierce理想 Ko群 置换环 |
| 英文关键词:Pierce ideal, K0 group, Exchange ring |
| 基金项目: |
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| 中文摘要: |
| 环R的理想P称为Pierce理想,如果R/p是R的Pierce茎.令Pier(R):{P | P是R的Pierce理想}.可证Pier(R)是拓扑空间.若R是幂等元中心的置换环,则Ko(R)≌{f:Pier(R)→Z|f,是连续的). |
| 英文摘要: |
| An ideal $P$ of a ring $R$ is said to be a Pierce ideal provided that $R/P$ is a Pierce stalk of $R$.
Let ${\rm Pier}(R)=\{P\ |\ P\ \mbox{is a Pierce ideal of}\ R\}$. It is
shown that ${\rm Pier}(R)$ is a topological space. If $R$ is an exchange
ring with all idempotents central, $K_0(R)\cong \{ f:{\rm Pier}(R)\to {\Bbb Z}\,\mid f\ \mbox{is continuous}\}$ is proved. |
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